Analyze the results of an experiment using simulations

Learning Objectives Define what a simulation is and explain its purpose in analyzing experiments. Design a simple simulation to model a real-world event with equally likely outcomes. Conduct trials of a simulation and systematically record the results. Calculate the frequency and relative frequency of outcomes from a simulation. Express experimental probabilities as rational numbers (fractions, decimals, or percentages). Compare simulated results to theoretical probabilities for simple chance events. Draw conclusions about the likelihood of events based on simulation data. Ever wonder how scientists predict the chance of rain or how likely you are to win a game? 🎲 We can use math to 'play out' events and guess what might happen! In this lesson, you'll lear...

TermDefinitionExample ExperimentA procedure carried out to gather data about an event or phenomenon.Flipping a coin 10 times and recording whether it lands on heads or tails. SimulationA model used to imitate a real-world situation or experiment, often when the real experiment is too difficult, costly, or time-consuming to perform.Using a coin flip to simulate the gender of a baby (Heads = Boy, Tails = Girl). TrialOne repetition or instance of an experiment or simulation.Each time you flip the coin in a simulation, that is one trial. OutcomeA possible result of a single trial in an experiment or simulation.When rolling a standard die, the outcomes are 1, 2, 3, 4, 5, or 6. FrequencyThe number of times a specific outcome occurs in a series of trials during a simulation.If 'Heads'...

Calculating Frequency \text{Frequency} = \text{Count of specific outcome} Use this rule to count how many times a particular result happened during your simulation trials. Calculating Relative Frequency (Experimental Probability) \text{Relative Frequency} = \frac{\text{Frequency of Outcome}}{\text{Total Number of Trials}} This rule helps you express how often an event occurred as a part of the whole experiment, often as a fraction, decimal, or percentage (rational numbers). Converting Rational Numbers \text{Fraction } \frac{a}{b} = a \div b \text{ (Decimal)}; \text{ (Decimal)} \times 100\% \text{ (Percentage)} Use this to convert your experimental probabilities into different forms of rational numbers for easier comparison and understanding.